MathDB

Let

\triangle ABC

be an acute-angled triangle with altitudes

AD

and

BE

meeting at

H

. Let

M

be the midpoint of segment

AB

, and suppose that the circumcircles of

\triangle DEM

and

\triangle ABH

meet at points

P

and

Q

with

P

on the same side of

CH

A

. Prove that the lines

ED, PH,

and

MQ

all pass through a single point on the circumcircle of

\triangle ABC

Problem Statement